$η^{(\prime)}\toπ^+π^-l^+l^-$ decays in the NJL model

TL;DR

An 3-5 sentence summary: The paper addresses the problem of accurately predicting eta and eta-prime decays to pi+ pi- l+ l- within the NJL model, focusing on chiral anomaly contributions and vector-meson exchanges. It combines box anomaly terms, rho-mediated triangular diagrams, and meson-loop corrections with an off-shell transition form-factor treatment, using a cutoff and constituent quark masses. The authors compute branching fractions for eta and eta-prime decays into electron and muon pairs and compare with BESIII and PDG data, finding that including meson loops and double-vector-dominance improves agreement, especially for muon channels. The study demonstrates that vector dominance naturally arises in the NJL framework and has implications for future eta/eta-prime physics programs at REDTOP, HIAF, and other facilities.

Abstract

The Nambu-Jona-Lasinio model is used to calculate the branching fractions of two-lepton decays $η^{(\prime)}\toπ^+π^-l^+l^-$, where $l=e,μ$. Particular attention is paid to the study of the contribution of the diagram with the exchange of two vector mesons. It is shown that taking this contribution into account is essential for the agreement between theoretical calculations and available experimental data.

Figures (2)

• Figure 1: The box diagram describing direct production of final states and the triangle quark-loop diagram in the NJL model with the gauge-covariant $\pi a_1$ and $\eta^{(\prime)}f_1$ diagonalizations.
• Figure 2: Triangular quark-loop diagrams contributing to decays $\eta^{(\prime)} \to\pi^+ \pi^- l^+l^-$.